Related papers: E-infinity structures over L-algebras
Leibniz algebras are certain generalization of Lie algebras. It is natural to generalize concepts in Lie algebras to Leibniz algebras and investigate whether the corresponding results still hold. In this paper we introduce the notion of…
We present a generalization of the notion of an algebra norm relevant to real finite-dimensional unital associative algebras. Among other things, this leads to a novel set of algebra isomorphism invariants, some of which are computationally…
The homotopy groups of a space are endowed with homotopy operations which define the \Pi-algebra of the space. An Eilenberg-MacLane space is the realization of a \Pi-algebra concentrated in one degree. In this paper, we provide necessary…
We develop the theory of probabilistic variants of the one-category and diagonal topological complexity, which bound the classical LS-category and topological complexity from below. Unlike any other classical or probabilistic invariants,…
Given any K\"ahler manifold $X$, Kapranov discovered an $L_\infty[1]$ algebra structure on $\Omega^{0,\bullet}_X(T^{1,0}_X)$. Motivated by this result, we introduce, as a generalization of $L_\infty[1]$ algebras, a notion of $L_\infty[1]$…
We provide a structural analysis for McCarthy algebras, the variety generated by the three-element algebra defining the logic of McCarthy (the non-commutative version of Kleene three-valued logics). Our analysis will be conducted in a very…
The deformation complex of an algebra over a colored PROP P is defined in terms of a minimal (or, more generally, cofibrant) model of P. It is shown that it carries the structure of an L_\infty-algebra which induces a graded Lie bracket on…
We provide a simple construction of a Gerstenhaber-infinity algebra structure on a class of vertex algebras V, which lifts the strict Gerstenhaber algebra structure on BRST cohomology of V introduced by Lian and Zuckerman. We outline two…
A self-contained description of algebraic structures, obtained by combinations of various limit procedures applied to vertex and face sl(2) elliptic quantum affine algebras, is given. New double Yangians structures of dynamical type are in…
An R-algebra A is called E(R)-algebra if the canonical homomorphism from A to the endomorphism algebra End_RA of the R-module {}_R A, taking any a in A to the right multiplication a_r in End_R A by a is an isomorphism of algebras. In this…
This paper builds a general framework in which to study cohomology theories of strongly homotopy algebras, namely $A_\infty, C_\infty$ and $L_\infty$-algebras. This framework is based on noncommutative geometry as expounded by Connes and…
We define closed model category structures on different categories connected to the world of operad algebras over the category C(k) of (unbounded) complexes of k-modules: on the category of operads, on the category of algebras over a fixed…
In this paper, we shall provide a purely $\infty$-categorical construction of the mixed graded structure over Chevalley-Eilenberg complexes computing homology and cohomology of Lie algebras defined over a field $\Bbbk$ of characteristic…
We show that an A-infinity algebra structure can be transferred to a projective resolution of the complex underlying any A-infinity algebra. Under certain connectedness assumptions, this transferred structure is unique up to homotopy. In…
We define inductively a sequence of purely algebraic invariants - namely, classes in the Quillen cohomology of the Pi-algebra \pi_* X - for distinguishing between different homotopy types of spaces. Another sequence of such cohomology…
In part I of this work we studied the spaces of real algebraic cycles on a complex projective space P(V), where V carries a real structure, and completely determined their homotopy type. We also extended some functors in K-theory to…
The classical problem of algebraic models for homotopy types is precisely stated, to our knowledge for the first time. Two different natural statements for this problem are produced, the simplest one being entirely solved by the notion of…
We give an elementary proof of the Eilenberg-Mac Lane trace isomorphism between the third 2-abelian cohomology group and quadratic forms. Our approach yields explicit constructions and we characterize when quadratic forms can be expressed…
Multialgebras (or hyperalgebras, or non-deterministic algebras) have been very much studied in Mathematics and in Computer Science. In 2016 Carnielli and Coniglio introduced a class of multialgebras called swap structures, as a semantic…
This paper introduces the notions of atoms and atomicity in $C$-algebras and obtains a characterisation of atoms in the $C$-algebra of transformations. Further, this work presents some necessary conditions and sufficient conditions for the…